Simplify the following expression: $x = \dfrac{-3r^2 - 45r - 168}{r + 7} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-3$ , so we can rewrite the expression: $ x =\dfrac{-3(r^2 + 15r + 56)}{r + 7} $ Then we factor the remaining polynomial: $r^2 + {15}r + {56} $ ${7} + {8} = {15}$ ${7} \times {8} = {56}$ $ (r + {7}) (r + {8}) $ This gives us a factored expression: $\dfrac{-3(r + {7}) (r + {8})}{r + 7}$ We can divide the numerator and denominator by $(r - 7)$ on condition that $r \neq -7$ Therefore $x = -3(r + 8); r \neq -7$